reserve F for Field,
  x for Element of F,
  V for VectSp of F,
  v for Element of V;

theorem
  for G being Abelian add-associative non empty addLoopStr, u,v,w
  being Element of G holds u - v - w = u - w - v
proof
  let G be Abelian add-associative non empty addLoopStr, u,v,w be Element of
  G;
  thus u - v - w = u + -v + -w .= u + -w + -v by RLVECT_1:def 3
    .= u - w - v;
end;
